Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

Abstract

We explore a formulation of thermodynamic geometry of black holes and prove that the divergent points of the specific heat correspond exactly to the singularities of the thermodynamic curvature. We investigate this correspondence for different types of black holes. This formulation can also be applied to an arbitrary thermodynamic system.

10 pages, 4 figures, typos fixed, references added

References in corpus (6)

• Geometrothermodynamics of black holes
• Thermodynamical Metrics and Black Hole Phase Transitions
• Thermodynamic Geometry of Fractional Statistics
• Thermodynamics of phantom black holes in Einstein-Maxwell-Dilaton theory
• A Commentary on Ruppeiner Metrics for Black Holes
• Condensation of an ideal gas obeying non-Abelian statistic

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